/* nag_real_sparse_eigensystem_sol (f12acc) Example Program. * * Copyright 2005 Numerical Algorithms Group. * * Mark 8, 2005. */ #include #include #include #include #include static void av(Integer, double, double *, double *); static void mv(Integer, double *, double *); static void my_dpttrf(Integer, double *, double *, Integer *); static void my_dpttrs(Integer, double *, double *, double *); int main(void) { /* Constants */ Integer licomm = 140, imon = 0; /* Scalars */ double estnrm, h, rho, sigmai = 0.0, sigmar = 0.0; Integer exit_status, info, irevcm, j, lcomm, n, nconv, ncv; Integer nev, niter, nshift, nx; /* Nag types */ NagError fail; /* Arrays */ double *comm = 0, *eigvr = 0, *eigvi = 0, *eigest = 0, *md = 0, *me = 0; double *resid = 0, *v = 0; Integer *icomm = 0; /* Pointers */ double *mx = 0, *x = 0, *y = 0; exit_status = 0; INIT_FAIL(fail); printf( "nag_real_sparse_eigensystem_sol (f12acc) Example Program Results\n"); /* Skip heading in data file */ scanf("%*[^\n] "); /* Read problem parameter values from data file. */ scanf("%ld%ld%ld%lf%*[^\n] ", &nx, &nev, &ncv, &rho); n = nx * nx; lcomm = 3*n + 3*ncv*ncv + 6*ncv + 60; /* Allocate memory */ if (!(comm = NAG_ALLOC(lcomm, double)) || !(eigvr = NAG_ALLOC(ncv, double)) || !(eigvi = NAG_ALLOC(ncv, double)) || !(eigest = NAG_ALLOC(ncv, double)) || !(md = NAG_ALLOC(n, double)) || !(me = NAG_ALLOC(n, double)) || !(resid = NAG_ALLOC(n, double)) || !(v = NAG_ALLOC(n * ncv, double)) || !(icomm = NAG_ALLOC(licomm, Integer))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Initialise communication arrays for problem using nag_real_sparse_eigensystem_init (f12aac). */ nag_real_sparse_eigensystem_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail); if (fail.code != NE_NOERROR) { printf( "Error from nag_real_sparse_eigensystem_init (f12aac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Set the mode. */ /* Select the mode using nag_real_sparse_eigensystem_option (f12adc). */ nag_real_sparse_eigensystem_option("REGULAR INVERSE", icomm, comm, &fail); /* Select the problem type using nag_real_sparse_eigensystem_option (f12adc). */ nag_real_sparse_eigensystem_option("GENERALIZED", icomm, comm, &fail); /* Construct M, and factorize using my_dpttrf. */ h = 1.0 / (double)(n + 1); for (j = 0; j <= n - 2; ++j) { md[j] = h * 4.0; me[j] = h; } md[n - 1] = h * 4.0; my_dpttrf(n, md, me, &info); irevcm = 0; REVCOMLOOP: /* repeated calls to reverse communication routine nag_real_sparse_eigensystem_iter (f12abc). */ nag_real_sparse_eigensystem_iter(&irevcm, resid, v, &x, &y, &mx, &nshift, comm, icomm, &fail); if (irevcm != 5) { if (irevcm == -1 || irevcm == 1) { /* Perform y <--- OP*x = inv[M]*A*x using my_dpttrs. */ av(nx, rho, x, y); my_dpttrs(n, md, me, y); } else if (irevcm == 2) { /* Perform y <--- M*x. */ mv(nx, x, y); } else if (irevcm == 4 && imon == 1) { /* If imon=1, get monitoring information using nag_real_sparse_eigensystem_monit (f12aec). */ nag_real_sparse_eigensystem_monit(&niter, &nconv, eigvr, eigvi, eigest, icomm, comm); /* Compute 2-norm of Ritz estimates using nag_dge_norm (f16rac).*/ nag_dge_norm(Nag_ColMajor, Nag_FrobeniusNorm, nev, 1, eigest, nev, &estnrm, &fail); printf("Iteration %3ld, ", niter); printf(" No. converged = %3ld,", nconv); printf(" norm of estimates = %17.8e\n", estnrm); } goto REVCOMLOOP; } if (fail.code == NE_NOERROR) { /* Post-Process using nag_real_sparse_eigensystem_sol (f12acc) to compute eigenvalues/vectors. */ nag_real_sparse_eigensystem_sol(&nconv, eigvr, eigvi, v, sigmar, sigmai, resid, v, comm, icomm, &fail); /* Print computed eigenvalues. */ printf("\n The %4ld generalized", nconv); printf(" Ritz values of largest magnitude are:\n\n"); for (j = 0; j <= nconv-1; ++j) { printf("%8ld%5s( %12.4f ,%12.4f )\n", j+1, "", eigvr[j], eigvi[j]); } } else { printf( " Error from nag_real_sparse_eigensystem_iter (f12abc).\n%s\n", fail.message); exit_status = 1; goto END; } END: NAG_FREE(comm); NAG_FREE(eigvr); NAG_FREE(eigvi); NAG_FREE(eigest); NAG_FREE(md); NAG_FREE(me); NAG_FREE(resid); NAG_FREE(v); NAG_FREE(icomm); return exit_status; } static void av(Integer nx, double rho, double *v, double *y) { /* Scalars */ double dd, dl, du, h, s; Integer j, n; /* Function Body */ n = nx * nx; h = 1.0 / (double)(n + 1); s = rho / 2.0; dd = 2.0 / h; dl = -1.0 / h - s; du = -1.0 / h + s; y[0] = dd * v[0] + du * v[1]; for (j = 1; j <= n - 2; ++j) { y[j] = dl * v[j-1] + dd * v[j] + du * v[j+1]; } y[n-1] = dl * v[n-2] + dd * v[n-1]; return; } /* av */ static void mv(Integer nx, double *v, double *y) { /* Scalars */ double h; Integer j, n; /* Function Body */ n = nx * nx; h = 1. / (double)(n + 1); y[0] = h*(v[0] * 4. + v[1]); for (j = 1; j <= n - 2; ++j) { y[j] = h*(v[j-1] + v[j] * 4. + v[j+1]); } y[n-1] = h*(v[n-2] + v[n-1] * 4.); return; } /* mv */ static void my_dpttrf(Integer n, double d[], double e[], Integer *info) { /* A simple C version of the Lapack routine dpttrf with argument checking removed */ /* Scalars */ double ei; Integer i; /* Function Body */ *info = 0; for (i = 0; i < n-1; ++i) { if (d[i] <= 0.0) { *info = i+1; goto END_DPTTRF; } ei = e[i]; e[i] = ei/d[i]; d[i+1] = d[i+1] - e[i]*ei; } if (d[n-1] <= 0.0) { *info = n; } END_DPTTRF: return; } static void my_dpttrs(Integer n, double d[], double e[], double b[]) { /* A simple C version of the Lapack routine dpttrs with argument checking removed and nrhs=1 */ /* Scalars */ Integer i; /* Function Body */ for (i = 1; i < n; ++i) { b[i] = b[i] - b[i-1]*e[i-1]; } b[n-1] = b[n-1]/d[n-1]; for (i = n-2; i >= 0; --i) { b[i] = b[i]/d[i] - b[i+1]*e[i]; } return; }